3-Coloring Graphs on Torus
Thesis title in Czech: | 3-barevnost grafů na toru |
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Thesis title in English: | 3-Coloring Graphs on Torus |
Key words: | barvení, grafy, torus |
English key words: | coloring, graph, torus |
Academic year of topic announcement: | 2015/2016 |
Thesis type: | diploma thesis |
Thesis language: | angličtina |
Department: | Computer Science Institute of Charles University (32-IUUK) |
Supervisor: | prof. Mgr. Zdeněk Dvořák, Ph.D. |
Author: | hidden - assigned and confirmed by the Study Dept. |
Date of registration: | 23.02.2016 |
Date of assignment: | 23.02.2016 |
Confirmed by Study dept. on: | 03.03.2016 |
Date and time of defence: | 06.09.2017 09:00 |
Date of electronic submission: | 20.07.2017 |
Date of submission of printed version: | 20.07.2017 |
Date of proceeded defence: | 06.09.2017 |
Opponents: | doc. Mgr. Robert Šámal, Ph.D. |
Guidelines |
The famous Grötzsch theorem stating that every planar triangle-free graph is 3-colorable motivates the study of the problem on other surfaces. The first surface for that the complete characterization of non-3-colorable triangle-free graphs is not known is torus. The goal of the thesis is to fill in this gap and to provide such a characterization (at least a partial one). |
References |
Bojan Mohar and Carsten Thomassen: Graphs on surfaces, Johns Hopkins University Press, 2001.
C. Thomassen: Grötzsch′s 3-Color Theorem and Its Counterparts for the Torus and the Projective Plane, Journal of Combinatorial Theory, Series B 62 (2), 1994, 268-279. Zdeněk Dvořák, Bernard Lidický: 4-Critical Graphs on Surfaces Without Contractible (<=4)-Cycles. SIAM J. Discrete Math. 28(1), 2014, 521-552. další časopisecká |